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GKEL_IGARSS_2011.ppt

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Dd Generalized Optimal Kernel-based Ensemble Learning for HS Classification Problems Prudhvi Gurram, Heesung Kwon Image Processing Branch U.S. Army Research Laboratory
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Current Issues Sample Hyper spectral Data (Visible + near IR, 210 bands) Grass Military vehicle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Training Data SVM 1 Decision Surface f 1 Kernel–based Ensemble Learning (Suboptimal technique) Random Subsets of spectral bands Ensemble Decision SVM 2 Decision Surface f 2 SVM 3 Decision Surface f 3 SVM N Decision Surface f N Majority Voting Sub-classifiers Used: Support Vector Machine (SVM) Random subsets of spectral bands ,[object Object],[object Object],[object Object],[object Object]
Training Data Random Subsets of Features (random bands) Combined Kernel Matrix SVM 2 SVM N Sparse Kernel-based Ensemble Learning (SKEL) ,[object Object],[object Object],[object Object],SVM 1 SVM 2 Optimal subsets useful for the given task
Optimization Problem Optimization Problem (Multiple Kernel Learning, Rakotomamonjy at al) : L1 norm Sparsity
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Generalized Sparse Kernel-based Ensemble (GKEL)
Sparse SVM Problem ,[object Object],[object Object],Primal optimization problem: * Tan et al, “Learning sparse SVM for feature selection on very HD datasets,” ICML 2010 ,[object Object],[object Object]
Dual Problem of Sparse SVM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Relaxation into QCLP ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Illustrative Example (Yisong Yue, “ Diversified Retrieval as Structured Prediction, ” ICML 2008) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],(Yisong Yue, “ Diversified Retrieval as Structured Prediction, ” ICML 2008)
[object Object],[object Object],[object Object],[object Object],[object Object],(Yisong Yue, “ Diversified Retrieval as Structured Prediction, ” ICML 2008)
[object Object],[object Object],[object Object],[object Object],[object Object],(Yisong Yue, “ Diversified Retrieval as Structured Prediction, ” ICML 2008)
Flow Chart Yes No Terminate ,[object Object]
Most Violated Features ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
How GKEL Works SVM 1 SVM 3 SVM 2 SVM N
Images for Performance Evaluation Forest Radiance I Desert Radiance II Hyperspectral Images (HYDICE) (210 bands, 0.4 – 2.5 microns) : Training samples
Performance Comparison (FR I) Single SVM SKEL (10 to 2 SVMs) GKEL (3 SVMs) (Gaussian kernel) (Gaussian kernel) (Gaussian kernel)
ROC Curves (FR I) ,[object Object],[object Object]
Performance Comparison (DR II) Single SVM GKEL (3 SVMs) SKEL (10 to 2 SVMs) (Gaussian kernel) (Gaussian kernel) (Gaussian kernel)
Performance Comparison (DR II) ,[object Object]
Performance Comparison SKEL: Initial SVMs: 25 After optimization: 12 GKEL: SVMs with nonzero weights: 14 ,[object Object],[object Object],Spambase Data
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Q&A ?
[object Object],[object Object],[object Object],[object Object],: Full-band diagonal Gaussian kernel the radius of the minimum enclosing hypersphere The margin of the hyperplane Optimally Tuning Kernel Parameters
Ensemble Learning Sub-classifier 1 Sub-classifier 2 Sub-classifier N Regularized Decision Function (Robust to noise and outliers) Ensemble decision -1 -1 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Training Data Random Subsets of Features (random bands) Combination of decision results SVM 2 SVM N SKEL : Comparison (Top-Down Approach) SVM 1 SVM 2
[object Object],[object Object],based on a limited number of active Iterative Approach to Solve QCLP ,[object Object],[object Object],[object Object]
Each Iteration of QCLP ,[object Object]
Iterative QCLP vs. MKL
Variable Length Features ,[object Object],[object Object],[object Object],[object Object],(e.g. 30%) leads to
GKEL Preliminary Performance Chemical Plume Data SKEL: Initial SVMs: 50 After optimization: 8 GKEL: SVMs with nonzero weights: 7 (22)
Relaxation into QCLP
QCLP
L1 and Sparsity Linear inequality constraints L2 Optimization L1 Optimization

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